Answer Happy

1) An experimental holographic media storage system uses a flexible photopolymer disk. The problem is that during rotation, the disk tilts, interfering with the information retrieval. To compensate, a laser beam is focused on the surface and the variations in the disk are measured in the reflections. A mirror is adjusted to align the disk and make retrieval possible. The transfer function for the mirror system is: 10 s 1950265024 GOLD The closed-loop specifications are zero steady-state error to step inputs (steady- state tracking), a 2% settling times of 0.5 seconds, and optimal damping. a) From the specifications for the closed-loop system, determine the location of the dominant poles. b) Use the following state representation of the system: -36 -33 -60 -36 -34 -60 37 34 61 C[ 0 10 10 ] Demonstrate that this system has the transfer given above. c) For the system in part b, assume that all the states are available to you, determine a state variable feedback controller with steady-state tracking and demonstrate that it works in MATLAB. d) For the system in part b, design a full-order observer to provide the states and demonstrate the performance of the closed-loop state-variable control system with steady-state tracking using MATLAB. e) For the system in part b, design a reduced-order observer and demonstrate the performance of the closed-loop state-variable control system with steady- state tracking using MATLAB.